Hierarchical decomposition heuristic for crude oil scheduling ...egon.cheme.cmu.edu/Papers/Cheninterfaces.pdfOptimal crude oil scheduling is critical to re neries. There are many varieties

INTERFACESVol. 00, No. 0, Xxxxx 0000, pp. 000–000

issn 0092-2102 |eissn 1526-551X |00 |0000 |0001

INFORMSdoi 10.1287/xxxx.0000.0000

c© 0000 INFORMS

Hierarchical decomposition heuristic for crude oilscheduling: a SINOPEC case

Xuan Chen, Dejing Chen, Simin Huang, Zhihai Zhang, Li ZhengDepartment of Industrial Engineering, Tsinghua University, Beijing 100084, China, [email protected],

[email protected], [email protected], [email protected], [email protected],

Ignacio GrossmannDepartment of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213-3890 USA, [email protected],

Shihui ChenSINOPEC Maoming Company, Maoming, Guangdong 525000, China, [email protected],

- This work addresses the large-scale crude oil scheduling problem of China’s SINOPEC Maoming refinery

importing various types of crude oil from two terminals via long-distance pipelines. A hierarchical decom-

position approach is employed to construct a two-stage MILP model of the practical refinery operations.

In the upper level model, storage and charging tanks are aggregated to determine the inflows and outflows

among the two terminals and the refinery. Detailed loading and unloading operations located on storage

and charging tanks are solved in the lower level sub-models. In order to further improve the computational

efficiency, we develop a practical rule-based tank selection strategy to efficiently obtain feasible detailed

schedules. While state-of-the-art commercial solvers cannot obtain a feasible solution of the relaxed mono-

lithic MILP model within reasonable time limit, the decomposition heuristic can obtain near-optimal and

flexible scheduling results with much less computational effort compared to the one obtained manually.

Key words : Crude oil scheduling, hierarchical decomposition, multiple terminals, long-distance pipelines

History :

1. Introduction

Crude oil scheduling is the first stage of the crude oil refining process. It involves crude oil unloading

from marine vessels to storage tanks, transfers and mixings in charging tanks, and a charging

schedule for each crude oil mixture to the crude distillation units (CDUs). Consequently, the

scheduling decision requires simultaneous selection of crude flows, allocations of vessels to tanks,

tanks to CDUs, and calculation of crude compositions.

Optimal crude oil scheduling is critical to refineries. There are many varieties of crude (e.g.,

light and heavy crude) in the market nowadays, varying widely in properties, processing difficulty

and product yields. Most refineries procure and process several types of crude that yield various

products and a wide range of profit margins. Optimal crude oil scheduling enables cost reduction

by using cheaper types of crude intelligently and minimizing crude changeovers. Kelly and Mann

1

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from Honeywell reported very large economic and operability benefits associated with better crude

oil blending scheduling (Kelly and Mann 2003a,b). Up to now, nevertheless, schedulers in most

Chinese refineries rely largely on their experience to make these decisions.

The Maoming Petrochemical Company, a subsidiary of China Petroleum & Chemical Corpora-

tion (referred to as SINOPEC in short), is the biggest petrochemical base in South China with an

annual crude oil processing capacity of 96.5 million barrels and annual ethylene processing capacity

of 300,000 million tons, as well as complete supporting systems of power supply, port handling,

railway transport, crude and product oil transfer pipelines and a 300,000 tonnage SBM (single buoy

mooring) offshore crude loading and unloading system. It mainly makes 30-odd types of products

including gasoline, kerosene, diesel oil, lube oil, solvent oil, naphtha, asphalt, ethylene, toluene,

PP, ethylene glycol, styrene, SBL and SBS. Fig. 1 depicts the refinery configuration. The refinery

branch consists of the Zhanjiang (Z) terminal, the Beisanling (B) terminal, the Maoming (M) refin-

ery plant and two crude transfer pipelines connecting two terminals and the plant, respectively the

Zhan-mao (ZM) pipeline and the Bei-mao (BM) pipeline. Terminal Z is state-owned and thus its

storage capacity for refinery M is limited. Terminal B, although with much higher storage capacity,

is not a natural deep-water terminal, hence the refinery built a SBM 30 kilometers away from

terminal B. Fifteen tanks located in terminal Z, terminal B and refinery M, respectively. Pipeline

ZM connecting terminal Z and refinery M is 110 kilometers long with the capacity of the pipeline

be about 143,000 barrels. Pipeline BM connecting terminal B and refinery M is 64 kilometers long

with the capacity of the pipeline be about 86,000 barrels. As both pipelines are long-distance, the

same flow pack injecting to and stripping out of pipeline ZM and BM are asynchronous. Moreover,

while pipeline BM is unidirectional, pipeline ZM is bidirectional, the reason of which is illustrated in

section Crude oil scheduling in the SINOPEC Maoming Company. Four CDUs and fifteen charging

tanks feeding crude oil to CDUs are located at the inland refinery plant M. Each CDU is designed

to process different types of crude with different specifications. In general, crude from terminal Z

feeds CDU1 and CDU2, while crude from terminal B charges CDU3 and CDU4. In case of crude

from terminal Z being not sufficient, CDU1 and CDU2 would process crude from terminal B. To

maintain steady production process, unless for planned temporary shutdown of production, each

CDU should be operating continuously and the processing rate should be within the lower and the

upper limit. Frequent changeovers and process rate fluctuations should also be avoided.

2. Crude oil scheduling in the SINOPEC Maoming Company2.1. Features of the refinery

Distinct features and practical operational constraints of the refinery are as follows.

Author: Article Short TitleInterfaces 00(0), pp. 000–000, c© 0000 INFORMS 3

Terminal Z: natural deep-water, capacity 2150,000 barrels CAPACITY LIMITED

Terminal B, capacity 4650,000 barrels

Refinery plant M, 4 CDUs 96.5 million barrels per year

single buoy mooring (SBM) CANNOT UNLOAD HIGH FUSION POINT CRUDE

(pipeline ZM) 110 km, 143,000 barrels

(pipeline BM) 64 km, 86,000 barrels

Figure 1 Configuration of the SINOPEC Maoming refinery.

• Crude storage segregation mode

— Unlike the illustrative examples in the literature, in our case it is required by the refinery

that tanks and pipelines should avoid undesirable mixture of different classes of types of crude

before feeding CDUs.

— It is ideal that only tanks storing the same type of crude or empty tanks receive crude from

vessels or pipelines. The detailed reason is explained in section Perspectives from the practitioners.

— In general, tanks and CDUs usually store or process only specific classes of types of crude,

as different types of crude vary significantly in properties and processability.

• Special treatment of crude oil transportation

— High pour point and high viscosity crude oil (denoted as HPHVC) cannot be stored in

storage tanks or be transported via the long-distance pipeline without special treatment (such as

heating up, blending with a specified proportion of light crude, or both).

— Thanks to its above-ground unloading lines and heating devices for storage tanks, HPHVC

can be unloaded at terminal Z. Due to the submarine pipeline connecting the SBM and terminal

B, however, HPHVC cannot unload at the SBM. Instead, other categories of crude oil including

light oil are mainly unloaded at terminal B.

— To safely transfer certain types of HPHVC from terminal Z to plant M, it is mandatory to

mix HPHVC with light crude in case of pipeline freezing. To be more specific, each type of high pour

point, high viscosity or high sulfur crude must be blended with a specified type of proportion of

light crude, determined by the laboratory branch of the refinery. The blending process is commonly

finished inside the long-distance pipeline, that is, multiple tanks storing different types of crude

would feed the pipeline simultaneously by taking into account the operational constraints. The

mixture of multiple types of crude inside the pipeline is denoted as a new type of crude.


• Bidirectional long distance pipeline

— Similar to the system in Reddy et al. (2004b,a), different types of crude arrive in either large

multi-parcel tankers or small single-parcel vessels. The capacity of terminal Z is limited, causing

this terminal to be the bottleneck of the system. Accordingly, very large scale vessels (VLCCs)

carrying large amounts of light crude from Middle East cannot unload to terminal Z. Therefore,

light crude needed in terminal Z is transferred from terminal B to plant M via pipeline BM, and

then from plant M to terminal Z via pipeline ZM conversely. The transfer operation from plant M

to terminal Z is called the backward transfer or the reverse transfer, which takes place about once

monthly. It follows that pipeline ZM is bidirectional.

— While pipeline BM is always operating as the transfer rate can be adjusted according to the

inventory level of the Plant M, pipeline ZM would occasionally shutdown because the capacity of

terminal Z is much smaller. Once shutdown, pipeline ZM should not fill with high viscosity crude

in order to avoid pipeline freezing. To insure that, an operation called cleaning transfer would

inject certain amount light crude into pipeline ZM to push out all the HPHVC inside the pipeline.

This segment of light crude, which would backtrack in case the follow-up operation is backward

transfer, is named as the cleaning crude.

— Since light crude seldom unloads at terminal Z, unless cleaning pipeline ZM or blending

with high pour point, high viscosity, and high sulfur crude, terminal Z would commonly not feed

light crude into pipeline ZM.

The overall process of the forward transfer, the pipeline stoppage, and the backward transfer is

shown in Fig. 2.

Period t-1

Period t

Current period outlet

Previous period

Period t+1

Period t+4

Current period inlet

Crude with high fusion point and high viscosity

Light crude Backward (light) crude

Figure 2 Transportation process of the bidirectional pipeline ZM.

2.2. Decision procedure of the refinery

Similar to the decision process described in Shah et al. (2009), there are two decision levels in

refinery M, namely the quarterly plan level and the ten-day plan level. Given demand forecasts, the


quarterly plan determines the variety and the volume of crude oil needed for the upcoming three

months, as well as the type and estimated quantities of final products to be ordered. Based on the

quarterly plan results, the ten-day plan determines the detailed schedule of unloading crude oil

from vessels into storage tanks, transporting crude oil among terminals and the plant, and feeding

the CDUs at various rates over time according to the production plan by taking into account the

operational constraints.

The current manual ten-day plan has the following shortcomings. First of all, it is complicated

and time consuming and thus not flexible enough to reschedule when supply chain disruptions

occur. Usually it takes hours to make the detailed crude oil schedule. Human errors and inconsis-

tencies are easily brought into the schedule. Secondly, since the schedule is made in a user-driven

simulation environment with the Aspen ORION system in the SINOPEC Maoming refinery, the

overall process cannot be optimized from a systematic perspective. Therefore, it was not rare to see

that the CDUs were running out of crude while the transportation of HPHVC was delayed because

of the lack of light crude, or the total amount of crude was sufficient but some of the CDUs had

to process the ”downgraded” type of crude. Besides, the manual scheduling results rely heavily on

the scheduler’s experience and skills, sometimes not easy to be used by shopfloor operators.

2.3. Problem definition

With the above introduction, we now state the multi-regional crude oil scheduling problem

addressed in the paper.

• Given:

— configuration of the refinery and the two terminals (numbers of CDUs, storage tanks, berths,

and interconnections among them), as shown in Fig. 1;

— builtin attributes of the system, including the set of types of crude, crude segregation mode

of storage and processing, upper and lower inventory levels of tanks, etc.;

— operational parameters of the system, including the start and the end time of the scheduling

horizon, the minimum crude settling time, limits on the number of simultaneously connected tanks

for all operations, flowrate limits for all operations and resources, etc.;

— initial state of the system, involving initial distribution of crude inside pipeline ZM (BM)

and the initial transfer direction, initial crude types and initial inventory levels of terminal and

refinery tanks, initial crude type of distillation and processing rate of each CDU, etc.;

— input of the system: information of vessels at each terminal, including arrival times, crude

types, volumes, and the unloading sequence of their parcels, updated in real time according to

crude suppliers and shipping companies;


— output of the system: production plan of each CDU passed down from higher level planning

decisions;

— economic parameters such as unit costs of different operations and crude distillation profits.

• Determine:

— detailed unloading schedule for each vessel;

— inventory levels and composition profiles of storage and charging tanks during the scheduling

horizon;

— detailed transfer schedule of pipeline ZM/BM, including the cleaning and reverse transfer

operations;

— detailed crude feeding profiles for CDUs.

• Objectives:

— maximize the total crude distillation profit;

— minimize the waiting time, and consequently the demurrage cost of each vessel;

— reduce the number of changeovers of tanks, piplines and CDUs;

— reduce the number of undesirable blending of different varieties of crude;

• Operational rules:

— There are broadly five categories of operating rules (constraints): safety rule, interconnection

rules, sequence rules of operations, mass and crude composition balance, and capacity limits. Some

of the detailed constraints are described in Appendix A.

In sum, we study a scheduling scheme (Fig.1) that is quite different from previous work reported

in the literature. The system consists of multiple regions distributing and sharing crude through

long-distance, possibly bidirectional pipelines. Mixing different varieties of crude oil should be

avoided (except for required blending) before delivering to CDUs. HPHVC can only be unloaded,

transferred, or processed with special treatment.

The above mentioned practical constraints along with the long-distance pipeline feature are very

difficult to model. Furthermore, the inherent large-scale combinatorial feature poses a challenge for

solving the model. The various types of crude processed (up to 20), the number of CDUs (4 CDUs,

each is designed to distill different crude types), and the number of storage and charging tanks (45

tanks in total) are very large in this case, making the problem computationally intractable. Hence,

we aim at obtaining satisfactory and flexible solutions of the problem robustly (within tolerable

time limits).


3. Perspectives from the practitioners

Crude oil scheduling in real-life plants exhibits features that are very different from the common

assumptions used in the literature. In this section, we present some of our industrial collaborators’

viewpoints based on their operating and management experiences of real-life plants.

3.1. The objective function

The crude oil scheduling problem is inherently multi-objective. The pioneering work Lee et al.

(1996) tried to minimize operational cost including sea waiting cost and unloading cost of marine

vessels, inventory cost, and CDU changeover cost. Magalhaes and Shah (2003) minimized the devi-

ation of the planned and the scheduled amounts for crude when solving the crude oil scheduling

problem in PETROBRAS’ REFAP refinery, Brazil. Mouret et al. (2010) focused on maximizing

crude distillation profit for the current scheduling period, as required by TOTAL, France. Reddy

et al. (2004b,a) studied the crude oil scheduling problem of coastal refineries based on the infor-

mation provided by the Singapore Refining Company, Singapore. They took into account of both

profit and operational cost. When executing the obtained schedules, more operational costs are

incurred, such as the changeover costs of tanks and pipelines, utility costs of storing and trans-

ferring crude oil, waste costs the result from undesirable mixture of crude, etc. It is in general

unrealistic to include them all in the objective function, as many of these objectives are difficult

to be expressed in economic terms. For instance, in a recent work (Shah and Ierapetritou 2011),

the crude oil scheduling problem incorporating with logistic constraints is considered. However,

one can observe that too many penalty items are added to the objective function, in which the

weight coefficients are difficult to determine in real-life plants. Other than that, assuring continuous

and smooth production of the refinery is considered to be the primary goal. That is to say, were

CDU demands not be satisfied, the objectives aiming at reducing operational cost, such as the

minimization of pipeline changeovers and the minimization of undesirable crude mixtures, are not

relevant. From the viewpoint of the plant manager, a schedule that satisfies all the demands with

minor unnecessary mixture is undoubtedly preferable than another schedule that avoids mixture

without fulfilling production demands. This reflects the feature that more soft constraints exhibit

in real world problems instead of purely hard mathematical constraints. The insight is that these

objectives are hierarchical with different priorities. As a matter of fact, it would not be appropriate

to optimize them simultaneously. Rather, different objectives with different priorities should be

optimized within different levels.

• Safety issues should always be the highest priority. For instance, continuous operations of units

should be guaranteed, the temperature of the crude inside the pipeline should not below its fusion

point, etc.


• Demand or customer orders should be satisfied, including the demand flow among the inner

sub-systems. With this as the prerequisite, different types of crude should be distilled intelligently

to make as much profit as possible.

• Operational costs incurred from unload, storage, transfer, and charge operations should be

minimized. This includes vessel demurrage cost, utility cost, undesirable crude mixtures cost,

changeover cost, etc.

Moreover, feasibility besides global optimality is one of the major concerns in practice. Feasi-

bility can be defined as ”to satisfy the planning decisions” or ”to distill different types of crude

on their corresponding most profitable CDUs”. Consequently a more straightforward way is to

firstly balance and optimize the amount of crude inflow and outflow globally, of which the math-

ematical model is able to efficiently obtain global optimal solutions. Detailed scheduling with a

large number of discrete decisions, of which the current linear programming based optimization

method cannot give optimal or even feasible solutions with limited computation effort, can be solved

locally or heuristically to yield near-optimal solutions within distinctly less CPU time. This kind of

methodology mimics the practical two level planning-scheduling decision process. Therefore, it is

more intuitive to schedulers. The key ingredient lies on how to reasonably incorporate the relaxed

scheduling constraints into the upper level planning model in order to avoid over-optimization of

the planning layer and infeasibility of the lower level problem.

3.2. Time representation

During the last two decades, research in the process system engineering (PSE) field has developed

various methods of representing temporal constraints. These methods are broadly categorized into

the discrete time representation and the continuous time representation, depending on whether

the events of the schedule can only take place at certain predefined time points, or can occur at

any moment during the time horizon. A comprehensive review is given in Mendez et al. (2006).

As pointed out in Wassick and Ferrio (2011), industrial practitioners tend to use the discrete-time

representation as it is simple and applicable to general processes. Also, according to our industrial

collaborators, in large-scale systems such as the SINOPEC Maoming refinery, start and end times

of tasks or operations given by continuous time models cannot be executed exactly at these time

points. Based on our computational experience, we also favor the discrete time representation for

complex systems more than its continuous time representation counterparts.

3.3. Handling with crude oil blending

In the following we explain why the SINOPEC Maoming refinery tends to avoid crude blending

before feeding CDUs, which introduces more discrete decision variables to the model, making the


Table 1 The crude-by-crude setting: a typical refining schedule for a CDU

crude Crude A Crude A/C 50%/50% Crude B+D mixture

Tank % T127 T127,50: T182,50, T129Tank vol 5722

start 2011-7-29 5:15 2011-7-29 22:00 2011-8-1 19:40end 2011-7-29 22:00 2011-7-31 14:23 2011-8-5 13:38

model more difficult to solve. Literature models usually utilize the blending setting to impose

constraints on tolerable upper and lower limits of the key component concentration, as stated in

equation (1) from Reddy et al. (2004b), where xkkc is a parameter of key component k ∈K in crude

c∈ C, FCTUiuct represents the amount of crude c∈ C delivered by tank i∈ I to CDU u∈ U during

period t ∈ T , and xkL/Uku are limits on the concentration of key component k ∈ K in feed to CDU

u∈ U , with IU the set of pairs (tank i, CDU u) such that i can feed crude to CDU u and IC the

set of pairs (tank i, crude c) such that i can hold crude c.

xkLkuFUut ≤

∑l

∑c

FCTUiuctxkkc ≤ xkUkuFUut, (i, u)∈ IU , (i, c)∈ IC. (1)

In the SINOPEC Maoming refinery, however, our industrial collaborators tend to use the crude-

by-crude setting. A typical refining schedule for a CDU is shown in Table 1, for which we need to

define the binary variable yiuct to indicate whether CDU u distills crude c from tank i during time

period t or not. Despite the large increase of number of binary variables, the advantage of the crude-

by-crude setting is that it conforms to the scheduler’s experience. When there are supply chain

disruptions, for instance late arrival of crude vessels, it would be much more intuitive and much

safer to modify the current schedule. On the contrary, although the blending setting incurs no extra

binary variables, the result given by the blending setting is confusing to the scheduler. It is known

that the mathematical programming models tend to set the variables to their bounds in order to

obtain better economic objective values. Once disruptions occur, for instance the insufficiency of a

certain type of crude or key component cause by the arrival delay of a vessel, the scheduler would

have to decrease the processing rate or even stop one of the units, incurring production stability

or even safety issues.

4. The decomposition framework

The crude oil scheduling problem is closely related to the batch process scheduling problem. Many

researchers have developed models and solution techniques for this class of problem, primarily


mixed integer linear or nonlinear programming (MILP or MINLP) models (Mendez et al. 2006).

Due to the complexity of the crude scheduling operations, however, large-scale MILP or MINLP

problems cannot be effectively solved. In the very beginning, we tried to apply different represen-

tations from the literature to the problem, for instance the discrete-time representation (Reddy

et al. 2004b), the synchronous continuous-time representation (Reddy et al. 2004a), and the unit

slot representation (Hu and Zhu 2007) (an extended formulation from the event-based model (Jia

et al. 2003)). We excluded constraints that make the problem difficult to model and solve, such

as the bidirectional feature of pipeline ZM, bilinear terms results from crude oil blending, and

unavoidable tank heels. Despite these simplifications, the state-of-the-art commercial MILP solvers

cannot provide a feasible solution for the large-scale monolithic model in several hours. In fact, we

were unable to obtain a feasible ten-day schedule of the refinery sub-problem without taking the

two terminals into consideration.

Although industrial applications based on mathematical programming techniques have been

reported in the literature (Mas and Pinto 2003, Magalhaes and Shah 2003), due to the complexity

of the crude scheduling operations, other exact and heuristic approaches have also been proposed,

such as the NLP approach (Fagundez et al. 2009), the event-tree search method (Zou et al. 2010),

combination of the MILP models and expert systems (Bok et al. 2002, Pan et al. 2009), model based

decomposition heuristics (Kelly 2002, Kelly and Mann 2004), random search method (Chryssolouris

et al. 2005), and Petri net-based heuristics that pre-assign a number of charging tanks to each

CDU (Wu et al. 2007, 2010). In this work, we resort to a hierarchical decomposition approach to

efficiently obtain a satisfactory solution of the large-scale and complex process.

To reduce the computational time, we break the monolithic model into two levels: (1) The

upper level problem that involves the transfer schedule of the long-distance pipelines and the

charging schedule of CDUs; (2) The lower level problem consists of three sub-problems, wherein

the Z problem involves the feeding and receiving schedule of tanks, and the unloading schedule

of parcels at terminal Z, the B problem involves the feeding and receiving schedule of tanks and

the unloading schedule of parcels at terminal B, and finally the M problem involves the feeding

and receiving schedule of tanks at refinery plant M. In principle, the upper level model makes

high level decisions of allocating crude resources among the refinery plant and two terminals in

a tank-aggregated way, while the lower level problem distributes these crude resources to specific

tanks. In practice we found that the upper level model for industrial problems can still not be

readily solved in reasonable time limit, notwithstanding its tank-aggregation simplification. This

motivates us to further separate the upper level model into pipeline transportation decisions, and


CDU charging decisions based on the observation that the two decisions are loosely linked. In

this way the upper level model consists of the Pipeline model and the CDU planning model. The

decomposition framework is shown in Fig. 3.

BM

ZMZ

B

Aggregated tank capacity

Lead time for pipeline transfer

Disaggregated crude demands

Max/minInventory level

Upper levelPipeline

Upper levelCDU

Lead time for vessel unload

Lower levelLower level

Figure 3 Decomposition framework of the SINOPEC refinery.

As in the upper level model, only the resource balance (among two terminals and the refinery

plant M) is considered without involving detailed operations of the storage and charging tanks.

The key point is to reasonably aggregate the demands of the refinery and two terminals. The basic

ideas of the upper level model are as follows.

• The storage and charging tank inventory capacity constraints are incorporated approximately

in a tank-aggregated way.

• A buffer time parameter of vessel unloading is employed to aggregate the supply of the termi-

nal.

• We introduce the lead time parameters of pipeline transportation and changeover to implicitly

handle with complex constraints of pipelines. The parameter of pipeline transportation lead time

denotes that the timing of each crude pack transported from the terminal to the refinery is adjusted

to take account of the transportation time, similar to Shah (1996). Complex constraints of pipelines

include that the HPHVC cannot stay inside the pipeline upon pipeline stoppage, and that the

amount and specifications of the reversely transferred light crude need to be determined.

Note that the choice of two parameters, namely V Tr, the maximal inventory ratio for all the charg-

ing tanks in the refinery, and SULBM/SULZM , the estimated vessel unloading lead time, has a

great impact on the aggregation of the terminal supply. With respect to the issue of determining

these parameters, we were notified by the refinery that: (1) the experienced scheduler of the refinery

would be able provide the model with fairly accurate parameters, in that restrictions are imposed


via the higher level production plan decisions, and that the scheduler is expert at the production

and scheduling details; (2) it provides more flexibility to the scheduler in the matter of adjusting

those parameters to accommodate production variations and supply disruptions, thus obtaining

more implementable, flexible, and profitable schedules. In fact, by adjusting these parameters and

leaving the generation of detailed schedules to computers, the scheduler can focus more on high-

level decisions. Instead of manually generating only one schedule in hours, the schedule is able to

generate several schedules in a matter of minutes and to choose the best one.

After the ”resource balance” stage, the primary objective of the lower level sub-problems is

to determine detailed tank operations, i.e., to allocate the (already known) resource demands on

certain tanks. Therefore, feasibility, other than optimality, is the major concern in the lower level

subproblem in that high level optimal decisions are obtained from the upper level model. As there

are a large number of discrete decision variables with triple indices (crude type c, tank i, time

period t), increasing the computational burden, a heuristic tank allocation policy is proposed based

on experience of the scheduler from the M refinery to obtain satisfactory and reliable results in

seconds. The proposed method did meet our industrial collaborators’ requirements by providing

them with near-optimal, flexible, and more implementable scheduling results in a short time.

The complete upper level MILP model is presented in Appendix A. The uniform discrete-time

representation is used. That it, the scheduling horizon is partitioned into NT identical periods

(t = 1,2, . . . ,NT ) with the time interval of each period be 6 hours. The main assumptions are as

follows: the change over time between different tasks at each unit is negligible; the crude flow in

any pipeline is plug flow; and crude mixing is perfect in long-distance pipelines. Furthermore, crude

is normally stored in floating roof tanks to minimize evaporation losses. Such a tank requires a

minimum crude level (or heel) to avoid damage to the roof, when the tank goes empty. Because of

the presence of the heel, crude usually accumulates in the tank over time. However, a crude type

with negligible volume fraction does not significantly affect the overall quality. Thus, to model the

rule that each tank can store at most one type of crude simultaneously while maintaining the heel,

the initial inventory in each tank in the proposed model equals the real inventory minus the heel,

and the maximum storage capacity equals the real capacity minus the heel, with the minimum

crude level be zero. In this way, linearity is maintained and the developed model corresponds to

an MILP problem.

Due to space issues, we do not include the lower level sub-problems. They are available upon

request. According to the schedule obtained by the upper level model, we can deduce when, where,

what type of crude and the amount of crude each region will receive or feed, by taking account


to the time lags of flow in and out of long-distance pipelines. We can also find out on the type

and amount of crude that each CDU processes during each period. Next, we solve the lower level

sub-models to obtain the detailed schedules, respectively.

Further decomposition. Despite the tank-aggregation simplification, the solution time of the

upper level model is still not acceptable for industrial problems. To further reduce the solution

time, we employ a spatial-based decomposition approach to the upper level model. The basic idea

is to solve the pipeline problem and the CDU planning problem separately. Firstly, the pipeline

problem treats the refinery as a demand node accumulating crude without consuming it. Then, the

CDU model allocates the accumulated crude resources to each CDU. To avoid crude shortage of

the CDU model, the deviation from the CDU production demand plan is minimized in the pipeline

problem.

Rule-based tank allocation algorithm. The lower level sub-problems can be solved by commercial

MILP solvers. However, the solution time is usually too long for industrial applications. Therefore,

we design rule-based tank allocation algorithms to solve the lower level sub-problems. Applying

these rule-based heuristics is a more practical choice for the industry. On the one hand, it has

limited impact on the optimality of the solution as economic objectives and demand balance are

the main issues in the upper level model. On the other hand, rule-based algorithms are able to

optimize lower level scheduling decisions, which sometimes are not readily modeled or solved.

From the perspective of practitioners, the rule-based heuristic algorithm is much more flexible

than mathematical models. The problem is solved with far less computational effort. In practice

the scheduling process or the operational rules might change, the scheduler can easily adjust the

algorithm interactively by adding new rules or deleting violated rules. Furthermore, due to tank

capacity shortage, the assumption that one tank can only store at most one type of crude at the

same time might not hold. Mathematical models based on this assumption would probably not

be computationally feasible. On the contrary, the proposed algorithm can be easily modified to

satisfy production demand by allowing minor crude mixtures in the same tank. For instance, if the

inventory level in a tank is relatively low and no other tank is available, the proposed algorithm

allows the tank to receive other types of crude. In this way, more flexible and more pragmatic

results are obtained.

5. Solutions and applications

A scheduling software implementing the approaches described in this work was implemented using

Excel VBA for the refinery. Two basic outputs of the software system are the Gantt charts and


the inventory profiles of vessels and tanks. Here we present the results of a real instance of the M

refinery (the first ten day period of December, 2009) that was solved on a Pentium M processor

with 1.60 GHz and 1.99GB memory using the upper level model, and the lower level sub-models

or the heuristic tank allocation algorithm. The data of the instance is available upon request. In

this scheduling period, CDU3 can be possibly shut down for annual inspection or keep processing.

The plant manager would like to analyze different scenarios to facilitate the decision making. This

provides an opportunity for the proposed method to easily generate two different schedules. The

actual schedule of the refinery made by the scheduler with the help of the spreadsheet-based Aspen

ORION system is to shut down CDU3.

1. All CDUs operate continuously, and each model is solved with XPRESS-MP 2008 with a gap

smaller than 1%. The upper level model consists of 9075 equations, 4133 variables and 1265

discrete variables. Note that the number of equations and discrete variables increases approxi-

mately linearly with the number of types of crude (10 for this case) and the number of periods

(40 for this case) used. The total CPU time of the four models is 1,873.8s (31.2min). Since

we can concurrently solve the three lower level sub-models, the total CPU time for solving the

problem is 1,361.7s (22.7min).

2. The upper level model is solved with XPRESS-MP 2008 for at most 600s, while the lower level

sub-problems are solved using the heuristic tank allocation algorithm.

• All CDUs operate continuously. The total CPU time is about 603s (the upper level model:

600s, the heuristic tank allocation algorithm: about 3s);

• CDU3 is shut down, and pipeline ZM does not transfer in reverse (the actual schedule of

the refinery): the total CPU time is about 603s (the upper level model 600s, and the heuristic

tank allocation algorithm about 3s). Fig. 4 shows the detailed schedule of refinery plant M

obtained by the proposed approach. An example of inventory level charts of tanks is displayed

in Fig. 5.

For the Gantt chart figures (implemented by Excel VBA), a cell block in the same color indicates

that during these periods, both the type and the amount of crude fed/received by the unit (parcel,

tank or CDU) do not change. Numbers in the cell indicate the flowrate, i.e., the amount of crude

transferred each period. F denotes Feed, R denotes Receive, U denotes Unload, Line 1 denotes

pipeline ZM, and Line 2 denotes pipeline BM. Different colors represent different types of crude.

As the solution time for large-scale problems is still too long, we apply the further decomposition

models and rule-based tank allocation algorithms to three scheduling horizons of the M refinery,

namely the last ten days of August, 2009, the middle and the last ten days of December, 2009.


Comparing to the currently adopted manual schedules, which would take an experienced scheduler

about one day with the help of the Aspen ORION system, the solution time of our approach is far

more efficient. The total number of changeovers of pipelines, tanks and CDUs reduces 19.05%.

Refinery M

Crude

CDU suitable

Name

Color

Time period 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Tank M-1

Tank M-2

Tank M-3 To CD U2 F23.75

Tank M-4

Tank M-5

Tank M-6 From Line2 R75

Tank M-7 From Line2 R75

Tank M-8

Tank M-9

Tank M-10

Tank M-11

Tank M-12

Tank M-13

Tank M-14

Tank M-15

To CDU4 F21.4 From Line2 R75 To CDU4 F40

To CDU4 F24 From Line2 R75

From Line1 R75 To CDU2 F17.86 To CDU2 F19.64 To CDU2 F21.61 From Line2 R75 To CDU2 F23.75

From Line2 R75 To CDU1 F23.75 From Line2 R31.67

From Line2 R75 To CDU4 F40

From Line1 R25

To CDU4 F28

To CDU4 F16 To CDU4 F13.5 From Line2 R50

To CDU4 F38.5 From Line2 R75 To CDU4 F40 From Line2 R75 To CDU4 F18.6

From Line1 R50 To CDU1 F23.75 From Line2 R75

From Line1 R46.88 To CDU1 F12

To CDU2 F20 To CDU2 F22 To CDU2 F19.84 To CDU2 F17.86 From Line2 R75

From Line2 R75 To CDU4 F40 To CDU4 F40 To CDU4 F26.5

To CDU4 F40 To CDU4 F12

To CDU2 F23.75

1

4 1 2 1 4 1

To CDU1 F21.86 From Line1 R28.12 To CDU1 F11.75

From Line2 R75 To CDU4 F40 From Line2 R43.33

From Line2 R25

2 2 1

SAL IRH+SAM WDR IRH+SLS SCQ IRL+SLS

OMN SAR SUD+XTJ

8 9 10

SAL IRH+SAM WDR IRH+SLS SCQ IRL+SLS IRL

IRL OMN SAR SUD+XTJ

2 3 4 5 6 7

4

Figure 4 Gantt chart of refinery plant M for case 2.

SUD+XTJ SUD+XTJ OMN

0

50

100

150

200

250

300

350

400

450

1 5 9 13 17 21 25 29 33 37 41 45 49

Inve

nto

ry

Period

Tank T129 395 IRH+SLS HEEL

IRH+SAM

SUD+XTJ

0

50

100

150

200

250

1 5 9 13 17 21 25 29 33 37 41 45 49

Inve

nto

r

Period

Tank T180 225 IRH+SAM HEEL

Figure 5 Example of the inventory level chart.

Author: Article Short Title

16 Interfaces 00(0), pp. 000–000, c© 0000 INFORMS

6. Conclusions

This study has focused on a multi-regional crude oil scheduling problem of the SINOPEC Maoming

refinery, which is quite different from case studies reported in the literature. A hierarchical decom-

position strategy for solving large scale problems was presented. We proposed a general two-stage

decomposition scheme that generates smaller tractable subproblems. Based on a uniform discrete-

time representation, the upper level model allocates different types of crude oil among multiple

regions to obtain the pipeline transportation plan and the CDU processing plan. The lower level

sub-models are solved next to obtain detailed schedules within each region. In order to further

improve the solution efficiency, we further decompose the upper level model into the pipeline trans-

portation plan model and the CDU processing plan model. A rule-based tank allocation algorithm

was adopted to obtain near-optimal schedules of the lower level sub-models. In a user-driven sim-

ulation environment using the Aspen ORION system, a schedule was obtained by experienced

schedulers in several hours. In contrast, the proposed method provided the refinery with near-

optimal, flexible, and more implementable scheduling results in minutes. Hence, the scheduler can

focus on high-level decisions and leave the generation of detailed schedules to computers.

Acknowledgments

This research was supported by National Science Foundation of China under grant 71071084.

AppendicesAppendix A The upper level model

We now present the upper level model using the decomposition framework shown in Fig. 3.

A.1 Nomenclature

Indices and Sets

B Set of tank b at terminal B

C Set of crude c

CL Set of light crude cL, CL ⊆C

CH Set of heavy crude cH , CH ⊆C

Cu Set of crude that can be processed by CDU u

M Set of tank m at refinery plant M

PA Set of parcel pA carried on vessels arriving at Jetty A of terminal Z

PB Set of parcel pB carried on vessels arriving at Jetty B of terminal Z

PC Set of parcel pC carried on vessels arriving at terminal B

PAC Set of (pA, c) satisfying that parcel pA carries crude c; PBC and PCC are similar


Interfaces 00(0), pp. 000–000, c© 0000 INFORMS 17

PAT Set of (pA, t) satisfying that PAT pA is no larger than t; PBT and PCT are similar

PAVA Set of (pA, vA) satisfying that pA is carried on vA; PBVB and PCVC are similar

T Set of period t, t= 1, 2, . . . , NT

U Set of CDU u

VA Set of vessel vA arriving at Jetty A of terminal Z

VB Set of vessel vB arriving at Jetty B of terminal Z

VC Set of vessel vC arriving at terminal B

VAT Set of (vA, t) satisfying that V AT vA is no larger than t; VBT and VCT are similar

Z Set of tank z at terminal Z

Parameters

BLrZM c1,c2 Proportion of c2 to c1 when pipeline ZM is transferring c1 (e.g. c1 is a blend of c2 and some

other type of crude, see Table 3 for an example)

PROFIT uc Unit profit of processing crude c in CDU u

CLRECZt′t Percentage of the crude fed to pipeline ZM by terminal Z in period t′, which will be ejected

back in period t, obtained by the upper level model; CLRECM t′t is similar

CRuU Upper limit on the fluctuation of processing rates of CDU u in two adjacent periods

CV V B Unit inventory cost of crude carried on vessels arriving at terminal B

FBML/U Lower and upper limit of the amount of crude transferred each period if in pipeline BM is

transferring

FCIBM ct Amount of crude c that must be fed to pipeline BM by tank yard at terminal B during period

t and will arrive at Refinery M, obtained by the upper level model; FCIMZct, FCIZM ct,

FCOBM ct, FCOMZct, and FCOZM ct are similar

FCLZM Amount of light oil fed to pipeline ZM each period when forwardly cleaning pipeline ZM;

FCLMZ is similar

FCUuct Amount of crude c fed to CDU u during period t, obtained from the upper level model

FIBM bL/U Lower and upper limit of the amount of crude fed each period by tank b if b connects to

pipeline BM

FIMZmL/U Lower and upper limit of the amount of crude fed each period by tank m if m connects to

pipeline ZM

FIZM zL/U Lower and upper limit of the amount of crude fed each period by tank z if z connects to

pipeline ZM

FMZL/U Lower and upper limit of the amount of crude transferred each period if in pipeline ZM is

reversely transferring

FOBMmL/U Lower and upper limit of the amount of crude received each period by tank m if m connects

to pipeline BM

FOMZzL/U Lower and upper limit of the amount of crude received each period by tank z if z connects

to pipeline ZM

FOZMmL/U Lower and upper limit of the amount of crude received each period by tank m if m connects

to pipeline ZM

FPTAL/U Lower and upper limit of the amount of crude unloaded each period if Jetty A at terminal

Z is unloading; FPTBL/U and FPTC

L/U are similar


18 Interfaces 00(0), pp. 000–000, c© 0000 INFORMS

FPT pAU Upper limit of the amount of crude unloaded each period if pA is unloading; FPT pB

U and

FPT pCU are similar

FPT bL/U Lower and upper limit of the amount of crude received each period by tank b if b connects

to unloading line; FPT zL/U and similar

FTUmuL/U Lower and upper limit of the amount of crude fed to CDU u by tank m each period if m

connects to u

FUuL/U Lower and upper limit of the amount of crude processed by CDU u

FUu0 Amount of crude processed by CDU u in the last period of the previous scheduling horizon

FZML/U Lower and upper limit of the amount of crude transferred each period if pipeline ZM is

forwardly transferring

MAXULTZ Maximum time lag between the arriving of a vessel at terminal and its fully unloading

NCT Minimum number of periods during which the type of crude transferred in a long-distance

pipeline does not change

NCXTB Maximum number of changeovers on each tank at terminal B; NCXTM and NCXTZ are

similar

NLL Maximum number of tanks at a tank yard connecting to a long pipeline at the same time

NPT Maximum number of tanks at a tank yard connecting to an unloading line at the same time

NTU Maximum number of tanks at refinery connecting to a CDU at the same time

PAT pA Arrival time of parcel pA, PAT pB and PAT pC are similar

PSpA Size of parcel pA, PSpB and PSpC are similar

SBM Safety time lag between flow in and out of pipeline BM (SBM <NT )

SCLZM Number of periods needed when cleaning pipeline ZM

SCT u Safety time lag between two changeovers on CDU u

SMZ Safety time lag between reverse flow in and out of pipeline ZM (SMZ <NT )

ST b Safety settling time of tank b after receiving crude; STm and ST zare similar

STM Largest safety settling time of each tank at Refinery M after receiving crude; STZ is similar

SULBM Safety transfer time of crude from any vessel just arriving at terminal B to tank yard at

Refinery M; SULZM is similar

SV M Safety inventory level for Refinery M at the end of the scheduling horizon

SV u Lower limit on the total inventory of crude which are suitable for processing in CDU u at

Refinery M at the end of the scheduling horizon

SV LCZ Safety inventory of light crude for terminal Z at the end of the scheduling horizon

SZM Safety time lag between forward flow in and out of pipeline ZM (SZM <NT )

V AT vA Arrival time of vessel vA; V AT vB and V AT vC are similar

V CT bc Initial inventory of crude c in tank b; V CTmc and V CT zc are similar

V SvA Size of vessel vA; V SvB and V SvC are similar

V T bL/U Lower and upper limit on the inventory level of tank b; V Tm

L/U and V T zL/U are similar

V Tr Upper limit on the utilization ratio of the total storage capacity of Refinery M

Variables

Binary variables


xbmt If refinery M is receiving crude from pipeline BM during period t and the crude comes from

terminal B, , then it equals 1, otherwise 0; xzmt (forwardly) and xmzt (reversely) are similar

xfcimzct If refinery M is feeding crude c reversely to pipeline ZM during period t in order to transfer

it to terminal Z, then it equals 1, otherwise 0; xfcobmct and xfcozmct are similar

xfctuuct If refinery M is feeding crude c to CDU u, then it equals 1, otherwise 0

xroizmt If during the latest transferring period before t (including t), pipeline ZM is forwardly

transferring, then it equals 1, otherwise 0

0-1 continuous variables

cxtuut If there is a changeover on CDU u at the start of period t, then it equals 1, otherwise 0

cxfcimzt If the type of crude fed to pipeline ZM by refinery M changes at the start of period t, then

it equals 1, otherwise 0; cxfcobmt and cxfcozmt are similar

cxfcuut If the type of crude processed in CDU u changes at the start of period t, then it equals 1

cxfimzt If refinery M starts or stops to feed crude to pipeline ZM at the start of period t, then it

equals 1, otherwise 0; cxfobmt and cxfozmt are similar

Continuous variables

fcibmct Total amount of crude c fed by tank yard at terminal B to pipeline BM during period t;

fcimzct, fcizmct, fcobmct, fcomzct, and fcozmct are similar

fcuuct Total amount of crude c fed to CDU u during period t

fibmt Total amount of crude fed by tank yard at terminal B to pipeline BM during period t; fimzt,

fizmt, fobmt, fomzt, and fozmt are similar

fuut Total amount of crude fed to CDU u during period t

rtimzt Latest period before t (including t) at which refinery M is reversely feeding crude to pipeline

ZM in order to transfer it to terminal Z

rtozmt Latest period before t (including t) at which refinery M is receiving crude which comes from

terminal Z from pipeline ZM

vctmct Total inventory of crude c in tank yard at refinery M at the end of period t

A.2 Model

In the upper level model, the scheduling objective is to maximize the crude processing profit and to

minimize changeovers of two pipelines. The coefficient CPIPESET in equation (A-) is the estimated

cost per pipeline changeover.

minimize∑u∈U

∑c∈C

∑t∈T

PROFIT uc · fcuuct +CPIPESET

∑t∈T

(cxfozmt + cxfobmt) (A-)

Constraints of the upper level model are listed below.

1. To insure pipeline transportation stability, once a new type of crude started to transfer in

pipeline ZM or pipeline BM, the transfer operation of this type of crude should last for at least

NCT periods. If the transfer state (i.e., forward transfer, reverse transfer, and stoppage) of

pipeline ZM (BM) changed at the beginning of period t, then cxfozmt (cxfobmt) equals to 1.


min{NCT,NT−t}∑k=0

cxfcozmt+k ≤ 1 t∈ T (A-a)


cxfcobmt+k ≤ 1 t∈ T (A-b)


cxfcimzt+k ≤ 1 t∈ T (A-c)

2. For feeding crude to CDUs, continuous variable fcuuct is defined as the amount of crude c

delivered to CDU u during time period t. It follow that fuut, the total amount of crude feeds

to CDU u during time period t should be within the processing limits of CDU u.

fuut =∑c∈C

fcuuct u∈U, t∈ T (A-a)

FUuL ≤ fuut ≤ FUu

U u∈U, t∈ T (A-b)

3. To maintain smooth production state, the total amount feeds to CDU u during each time period

is allowed to vary within the limits (±CRuU) from the previous period. The parameter FUu0

is the total feed to CDU u during the last period of the previous scheduling horizon.

(1−CRu

U)fuut ≤ fuu(t+1) ≤

(1 +CRu

U)fuut u∈U, 1< t<NT (A-a)(

1−CRuU)FUu0 ≤ fuu1 ≤

(1 +CRu

U)FUu0 u∈U (A-b)

4. During each time period, CDU u is allowed to process only one type of crude. Binary variable

xfctuuct being equal to 1 represents that CDU u processes crude type c during time period t.

FUuU ·xfctuuct ≥ fcuuct u∈U, c∈C, t∈ T (A-a)∑

c∈C

xfctuuct ≤ 1 u∈U, t∈ T (A-b)

5. The following constraints require that the processing of a type of crude should last for at least

SCT u time periods in CDU u before switching to another type. We further constrain that

the processing rate cannot change when processing the same type of crude to stabilize the

production process.

cxfcuut ≥ xfctuuct−xfctuuc(t−1) u∈U, c∈C, t > 1 (A-a)

cxfcuut ≥ xfctuuc(t−1)−xfctuuct u∈U, c∈C, t > 1 (A-b)

cxfcuu1 = 1 u∈U (A-c)min{SCTu−1,NT−t}∑

k=0

cxfcuu(t+k) ≤ 1 u∈U, t∈ T (A-d)


fuut− fuu(t−1) ≤ FUuU · cxfcuut u∈U, t > 1 (A-a)

fuu(t−1)− fuut ≤ FUuU · cxfcuut u∈U, t > 1 (A-b)

6. Before the end of period t, the total amount of crude in the tank yard at refinery M cannot

exceed the total maximum available storage capacity of all tanks. Parameter V Tr denoting the

maximal utilization of the overall storage capacity at refinery M is adopted to ensure feasibility

of the lower level problem. Parameter V CTmc is the initial inventory of crude type c in tank

m.

vctmct =∑m∈M

V CTmc +t∑

k=1

(fcozmck + fcobmck− fcimzck−

∑u∈U

fcuuck

)c∈C, t∈ T

(A-)

∑c∈C

vctmct ≤ V Tr ·∑m∈M

V TmU t∈ T (A-)

7. Practically, the accumulated inventory for crude type c at refinery M at the end of time period t,

defined as the left hand side (LHS) of (A-), should be above zero. For production robustness,

it is further required that the accumulated inventory at the end of each time period should be

sufficient to make sure that the processing in CDU u last for another SCT u time periods without

crude refill. Accordingly, the summation of item∑

u∈U fcuucs of the right hand side (RHS) of

(A-) is from 1 to t + SCT u − 1. Since each tank needs some time (STM) for brine settling

and removal after receiving crude in the detailed lower level decisions, both items fcozmck and

fcobmck are summed from 1 to t−STM .

∑m∈M

V CTmc +

t−STM∑k=1

(fcozmck + fcobmck)−t∑

j=1

fcimzcj ≥

min{t+SCTu−1, NT}∑s=1

∑u∈U

fcuucs c∈C, t>STM

(A-)

∑m∈M

V CTmc−t∑

j=1

fcimzcj ≥min{t+SCTu−1, NT}∑

s=1

∑u∈U

fcuucs c∈C, t≤ STM (A-)

8. Similar to the refinery setting, before the end of time period t, the total amount of each type of

crude received from terminal Z (terminal B) should not exceed the maximum available supply

at terminal Z (terminal B). For terminal Z, an extra constraint is required to guarantee that


the total amount of light crude transferred reversely to terminal Z should be enough to ensure

the safety transfer of high pour point, high viscosity, and high sulfur crude in pipeline ZM.

∑c′∈C

t∑k=1

fcozmc′k ·BLrZM c′c ≤∑z∈Z

V CT zc +∑

(pA,c)∈PAC,(pA,t−SULZM)∈PAT

PSpA

+∑

(pB ,c)∈PBC,(pB ,t−SULZM)∈PBT

PSpB +

t−SMZ−STZ∑s=1

fcimzcs c∈C, t > SMZ +STZ

(A-)

∑c′∈C

t∑k=1

fcozmc′k ·BLrZM c′c ≤∑z∈Z

V CT zc

+∑

(pA,c)∈PAC,(pA,t−SULZM)∈PAT

PSpA +∑

(pB ,c)∈PBC,(pB ,t−SULZM)∈PBT

PSpB , c∈C, t≤ SMZ +STZ

(A-)

t∑k=1

fcobmck ≤∑b∈B

V CT bc +∑

(pC ,c)∈PCC,(pC ,t−SULBM)∈PCT

PSpC c∈C, t∈ T (A-)

Since terminal Z may receive light crude from refinery M while terminal B does not, the

extra term BLrZM c′c in constraints (A-) and (A-) is not included in constraint (A-).

Parameter BLrZM c′c is the specified proportion of the amount of crude type c blending with

crude type c′ when transferring crude c′. If c′ and c are the same type of crude, then BLrZM c′c

equals to 1. If c′ is not light crude and c is light crude, then BLrZM c′c equals to the specified

proportion of the amount of c blending with the amount of c′ to guarantee transportation safety.

In other cases, BLrZM c′c equals to 0. For crude type c which is pure, parameters V CT zc,

V CT bc, PSpA , PSpB , and PSpC are the initial crude inventory levels or parcel sizes at terminal

Z or terminal B. For crude type c which is a blend, parameters V CT zc, V CT bc, PSpA , PSpB ,

and PSpC are computed as adjusted crude inventory levels or adjusted parcel sizes by taking

into account the proportion of each pure type of crude in the blend. A typical instance of

parameter BLrZM c′c is listed in Table 3, where crude type SUD XTJ is obtained by blending

70% of crude SUD with 30% of crude XTJ.

9. Before the end of period t, the total inventory level of light crude at terminal Z should be

above the safety inventory for cleaning pipeline ZM. There are three cases in which we need to

clean pipeline ZM: (1) forward transfer - stop - forward transfer, (2) forward transfer - reverse

transfer, and (3) forward transfer – stop until the end of the scheduling horizon. Since pipeline

ZM is allowed to transfer reversely at most once during the scheduling horizon, case (3) can


also happen at most once. We set the safety inventory level for cleaning pipeline ZM to be

the amount of light crude (SCLZM · FCLZM) for cleaning once. Besides, at the end of the

scheduling horizon, the total inventory level of light crude at terminal Z cannot be lower than

the safety inventory of light crude (SV LCZ) for terminal Z (light crude unloaded at terminal

Z is omitted). ∑c∈CL

t∑k=1

fcimzck ≥∑c∈CL

∑c′∈C

t∑s=1

fcozmc′sBLrZM c′c

−∑c∈CL

∑z∈Z

V CT zc +SCLZM ·FCLZM t∈ T(A-)

∑c∈CL

∑t∈T

(fcimzct−

∑c′∈C

fcozmc′t·BLrZM c′c

)+∑z∈Z

∑c∈CL

V CT zc ≥ SV LCZ (A-)

10. At the end of the scheduling horizon, the total inventory level of the types of crude for CDU

u cannot be below than the safety inventory SV u, and the total inventory level of all types of

crude cannot be under the total safety inventory SV M .∑c∈CU

vctmcNT ≥ SV u u∈U (A-a)∑c∈C

vctmcNT ≥ SV M (A-b)

11. Pipeline ZM can transfer forwardly at most one type of crude, pure or blended, during period t,

and the total amount of crude forwardly transferred during period t must be within the transfer

limits.

FZMU ·xfcozmct ≥ fcozmct c∈C, t∈ T (A-a)∑c∈C

xfcozmct ≤ 1 t∈ T (A-b)

fozmt =∑c∈C

fcozmct t∈ T (A-c)

FZML ·xzmt ≤ fozmt ≤ FZMU ·xzmt t∈ T (A-d)

12. Pipeline BM can transfer at most one type of crude during period t, and the total amount of

crude transferred during period t must be within the transfer limits.

fobmt =∑c∈C

fcobmct t∈ T (A-a)

FBML ·xbmt ≤ fobmt ≤ FBMU ·xbmt t∈ T (A-b)

FBMU ·xfcobmct ≥ fcobmct c∈C, t∈ T (A-c)∑c∈C

xfcobmct ≤ 1 t∈ T (A-d)


13. Pipeline ZM can transfer reversely at most one type of light crude during period t, and the

total amount of crude reversely transferred during period t must be within the transfer limits.

fimzt =∑c∈CL

fcimzct t∈ T (A-a)

FMZL ·xmzt ≤ fimzt ≤ FMZU ·xmzt t∈ T (A-b)

FIMZU ·xfcimzct ≥ fcimzct c∈C, t∈ T (A-c)∑c∈CL

xfcimzct ≤ 1 t∈ T (A-d)∑c∈CH

xfcimzct = 0 t∈ T (A-e)

14. Continuity constraints to assure the safe transportation of pipelines: When pipeline ZM (BM)

transfers continuously, the total amount of crude transferred during each period should be the

same. That is, if both xzmt and xzmt−1 equal to 1, then fozmt equals fozmt−1.

fozmt− fozmt−1 ≤ FZMU · (2−xzmt−xzmt−1) t > 1 (A-a)

fozmt−1− fozmt ≤ FZMU · (2−xzmt−xzmt−1) t > 1 (A-b)

fobmt− fobmt−1 ≤ FBMU · (2−xbmt−xbmt−1) t > 1 (A-c)

fobmt−1− fobmt ≤ FBMU · (2−xbmt−xbmt−1) t > 1 (A-d)

fimzt− fimzt−1 ≤ FMZU · (2−xmzt−xmzt−1) t > 1 (A-e)

fimzt−1− fimzt ≤ FMZU · (2−xmzt−xmzt−1) t > 1 (A-f)

15. If refinery M is feeding pipeline ZM during period t, then refinery M cannot receive any crude

from terminal Z via pipeline ZM during periods t + 1, t + 2, · · · , and t + SMZ + SZM . This

constraint is used to approximate the bi-directional feature of pipeline ZM instead of directly

model the movement of flows inside it.

(SMZ +SZM) ·xmzt +

min{SMZ+SZM,NT−t}∑k=0

xzm(t+k) ≤ SMZ +SZM t∈ T (A-)

16. Variables cxfozmt, cxfobmt, cxfcozmt, cxfcobmt, and cxfcimzt are defined as in the following

examples. If xzmt does not equal to xzmt−1 (pipeline ZM changes the transfer state from

forward transfer to stoppage (or reverse transfer), or from stoppage (or reverse transfer) to

forward transfer, at the beginning of period t), then cxfozmt ≥ 1. If xfcozmct does not equal

to xfcozmc(t−1) for any c (pipeline ZM changes the type of crude forwardly transferring at the

beginning of period t), then cxfcozmt ≥1.

cxfozmt ≥ xzmt−xzmt−1 t > 1 (A-a)


cxfozmt ≥ xzmt−1−xzmt t > 1 (A-b)

cxfozm1 = 0 (A-c)

cxfobmt ≥ xbmt−xbmt−1 t > 1 (A-d)

cxfobmt ≥ xbmt−1−xbmt t > 1 (A-e)

cxfobm1 = 0 (A-f)

cxfimzt ≥ xmzt−xmzt−1 t > 1 (A-g)

cxfimzt ≥ xmzt−1−xmzt t > 1 (A-h)

cxfimz1 = 0 (A-i)

cxfcozmt ≥ xfcozmct−xfcozmc(t−1) c∈C, t > 1 (A-j)

cxfcozmt ≥ xfcozmc(t−1)−xfcozmct c∈C, t > 1 (A-k)

cxfcozm1 = 0 (A-l)

cxfcobmt ≥ xfcobmct−xfcobmc(t−1) c∈C, t > 1 (A-m)

cxfcobmt ≥ xfcobmc(t−1)−xfcobmct c∈C, t > 1 (A-n)

cxfcobm1 = 0 (A-o)

cxfcimzt ≥ xfcimzct−xfcimzc(t−1) c∈C, t > 1 (A-p)

cxfcimzt ≥ xfcimzc(t−1)−xfcimzct c∈C, t > 1 (A-q)

cxfcimz1 = 0 (A-r)

17. Pipeline ZM can reversely transfer at most once during the scheduling horizon.

∑t∈T

cxfimzt ≤ 1 + (1−xmz1) (A-)

18. If pipeline ZM has just switched the transfer state from stoppage (stop after forward transfer)

to forward transfer, then the crude firstly ejected from pipeline ZM must be light crude. If

forward transfer lasts for less than SCLZM periods, then all the crude ejected from pipeline

ZM must be light crude, otherwise the type of crude ejected from pipeline ZM at the first

SCLZM periods should be light crude.

∑c∈CL

fcozmc(t+k) ≤ FCLZM ·(xzmt+k− cxfozmt+1 + 1

)t <NT, k = 1,2, . . . ,min{SCLZM,NT − t}

(A-)

∑c∈CL

fcozmc(t+k) ≥ FCLZM ·(xzmt+k + cxfozmt+1− 2 +xroizmt

)t <NT, k = 1,2, . . . ,min{SCLZM,NT − t}

(A-)

Here xroizmt is a binary variable defined as below: if pipeline ZM is forwardly transferring


during the latest period of transfer operations before period t (including t), then xroizmt equals

1, otherwise 0.

rtimz1 = xmz1 (A-a)

rtimzt ≥ rtimzt−1 t > 1 (A-b)

rtimzt ≤ rtimzt−1 + t ·xmzt t > 1 (A-c)

rtimzt ≥ t ·xfimzt t > 1 (A-d)

rtimzt ≤ t t > 1 (A-e)

rtozm1 = xzm1 (A-f)

rtozmt ≥ rtozmt−1 t > 1 (A-g)

rtozmt ≤ rtozmt−1 + t ·xzmt t > 1 (A-h)

rtozmt ≥ t ·xzmt t > 1 (A-i)

rtozmt ≤ t t > 1 (A-j)

NT ·xroizmt ≥ rtozmt− rtimzt t∈ T (A-k)

NT · (1−xroizmt)≥ rtimzt− rtozmt t∈ T (A-l)

19. Since pipeline ZM and BM are initially non-empty in the beginning of the scheduling horizon,

we have to take into account the initial holdup inside the long-distance pipelines. In light of

the fact that the model always ensures a safety inventory for each CDU in refinery M, initial

holdup in pipelines are not in emergent need by CDUs and we omit the initial holdup in the

upper level model. Decisions about when and where the initial holdup in long-distance pipelines

will be ejected are considered in lower level sub-models. However, we do have to restrain that

during the first SZM (SBM) periods of the scheduling horizon, refinery M cannot receive any

crude which is fed by terminal Z (B) during the scheduling horizon.

xzmt = 0 t≤ SZM (A-a)

xbmt = 0 t≤ SBM (A-b)

To sum up, the upper level model consists of expressions (A-) ˜ (A-b).

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Table 3 Example blending proportion BLrZMc′c for the pure and blend type of crude

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SUD XTJ 0.7 0.3 0 0 0 0IRH 0 0 0 0 0 0.5

SAM 0 0 0 0 0 0.5SAM IRH 0 0 0 0.5 0.5 0

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